Hillel is juggling flaming torches to raise money for charity. His initial appearance raises $\$500$, and he raises $\$15$ for each minute of juggling performance. The amount $R$ of money Hillel raises is a function of $t$, the length of his performance in minutes. Write the function's formula. $R=$
The amount of money Hillel raises for each minute of performance is constant, so we're dealing with a linear relationship. We could write the desired formula in slope-intercept form: $R= mt+ b$. In this form, $ m$ gives us the slope of the graph of the function and $ b$ gives us the $y$ -intercept. Our goal is to find the values of $ m$ and $ b$ and substitute them into this formula. We know that each minute of Hillel's performance raises $\$15$, so the slope $ m$ is ${15}$, and our function looks like $R={15}t+ b$. We also know that Hillel's initial appearance raises $\$500$, so the $y$ -intercept ${b}$ is ${500}$. Since ${m}={15}$ and ${b}={500}$, the desired formula is: $R={15}t+{500}$